We present recent progress in searching for galaxies at redshift from z ≃ 5 to z ̃ 10. Wide-field and sensitive surveys with 8m class telescopes have been providing more than several hundreds of star forming galaxies at z ̃ 5 - 7 that are probed in the optical window. These galaxies are used to study the early cosmic star formation activity as well as the early structure formation in the universe. Moreover, near infrared deep imaging and spectroscopic surveys have found probable candidates of galaxies from z ̃ 7 to z ̃ 10. Although these candidates are too faint to be identified unambiguously, we human being are now going to the universe beyond 13 billion light years, close to the epoch of first-generations stars; i.e., Population III stars. We also mention about challenges to find Population III-dominated galaxies in the early universe.